PHIL 689: Mathematical Logic (Spring 2003)

• Place and Time: MW 8:30-10:00
• Instructor: Robin Smith (rasmith@tamu.edu)
• Office thereof: Bolton 314
• Telephone thereat: 845-5696

The subject of this course is the metatheory of propositional and predicate logic. This will include definitions of formal languages for these systems, their proof theory, model theory, and demonstrations of their soundeness and completeness. As a necessary background for this, we will begin with an overview of the basic elements of set theory, including functions and relations, and a discussion of methods of mathematical proof.

Texts

• José L. Zalabardo, Introduction to the Theory of Logic. Westview Press, 1999. ISBN 0-8133-6602-X

Formal Work

1. Homework asssignments (8): 20%
2. Mid-term exam (take-home): 40%
3. Final exam (take-home): 40%

In addition, we will work through a number of proofs in class. Understanding the nature of proofs in logical theory is a fundamental aspect of this course, and students will occaisionally be asked to make presentations of proofs of theorems in class (with advance warning).

Schedule

Page numbers refer to Zalabardo. Although I will try to stay reasonably close to this schedule, the pace may need to be adjusted depending on how the class goes.

• Jan. 13,15:
  1. (Introductory remarks)
  2. Basic set theory (1.1-1.3, pp. 1-8)
• Jan. 20,22:
  1. (MLK, no classes)
  2. Mathematical proof; Relations and functions (1.4-1.7, pp. 8-32)
• Jan 27,29:
  1. Functions (1.7), numbers (1.8)
  2. Language PL: syntax (2.1-2.3, pp. 36-49)
• Feb. 3, 5:
  1. Syntactic metatheorems (2.2-2.3)
  2. Semantics of PL (2.4, pp. 49-55)
• Feb. 10, 12:
  1. Unique readability (2.5, pp. 55-60)
  2. Recursive Definitions, Expressive Completeness (2.6-2.7, pp. 60-68)
     MID-TERM EXAM DISTRIBUTED
• Feb. 17, 19:
  1. Expressively complete languages (2.8, pp. 69-75)
     MID-TERM EXAM DUE
  2. First-Order Logic (FOL): Syntax (3.1-3.2, pp. 76-90)
• Feb. 24, 26:
  1. FOL: Syntax (3.1-3.2, pp. 76-90)
  2. FOL: Semantics (3.3-3.4, pp. 90-101)
• Mar. 3, 5:
  1. FOL: Logical Consequence (3.5, pp. 102-108)
  2. FOL: Models (3.6, pp. 109-116)
• Mar. 10, 12: Spring Break
• Mar. 17, 19:
  1. FOL: Deductions--Basic and Connective Rules (4.1-4.2, pp. 117-122)
  2. FOL: Deductions--Propositional deduction (4.3, pp. 122-126)
• Mar. 24, 26:
  1. FOL: Deductions--Substitution (4.4, pp. 126-132)
  2. FOL: Deduction--Quantifiers (4.5, pp. 132-134
• Mar. 31, Apr. 2:
  1. FOL: Deducibility (4.6-4.7, pp. 134-140)
  2. FOL: Soundness (5.1, pp. 149-158)
• Apr. 7, 9:
  1. FOL: Completeness (5.2, pp. 158-162)
  2. FOL: Completeness (5.2, pp. 158-162), one more time
• Apr. 14, 16:
  1. FOL: Well-Rounded Sets (5.3, pp. 158-162)
  2. FOL: Negation Completeness (5.6, pp. 174-178)
• Apr. 21, 23:
  1. FOL: Compactness (5.9, pp. 187-188)
  2. FINAL EXAM DISTRIBUTED
• Apr. 28-May 5:
  1. Monday: (This day is actually "redefined" as a Friday; hence, there is no class).
  2. Wednesday: no class (Reading Day)
  3. Friday: FINAL EXAM DUE

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